The Great Houses are the most powerful of the noble houses of the Eight Kingdoms. They exercise immense authority and power over their vassals and territories and answer to only the King of the Eight Kingdoms. Before the Darkest Night, each of the Eight Kingdoms were ruled independently of each other by royal families. The families have stayed the same as they’ve served House Lannister for centuries.
It is currently unknown who is still a Great House and who is a Royal House, given the current events of the seating of a bastard on the throne.